In a heavy large saucepan, brown your chicken for a few minutes on each side with a little oil or cooking spray.
Add water, balsamic vinegar, soy sauce, sugar, garlic, and ginger and cook on high until the liquid starts to boil. Reduce heat & simmer, covered, for about 20 minutes.
Remove cover and bring heat to high once again. This will cause the sauce to reduce down and become a glaze - takes about 8 minutes. Turn your drumsticks occasionally during this process, and don't walk away! The glaze can quickly burn if not watched.
Transfer cooked chicken to a platter, and pour the remaining glaze on top. Serve with rice - the rice helps sop up the delicious juices!